Cost Function Networks (CFNs) offer a simple and general framework for modeling and solving constrained optimization problems which allows to deal with over-constrained problems as well as preferences between solutions. Most solving approaches for CFNs rely on complete tree search methods. Few attempts have been done to use local search approaches to solve CFNs. This chapter investigates the use of Variable Neighborhood Search (VNS) for CFNs. We present two VNS-based methods that use (partial) tree search inside its local neighborhood exploration. Then, we describe an iterative approach above VNS unifying two complete and incomplete search methods, by controlling two parameters, the discrepancy limit and the neighborhood size. Thus, optimality of the obtained solutions can be proven when the neighborhood size is maximal and with unbounded tree search. Finally, we perform experiments on several instances from the Computational Protein Design (CDP) problem, showing the practical benefit of our VNS-based approaches.